The second derivative test is much like the first derivative test. However, one must take the derivative of the derivative of the function. The second derivative allows one to find if a point is concave up or down. To find out if it is, plug in any given point into the second derivative. If it is positive, then it is concave up at that point. If it is negative, then the original function is concave down at that point. If the second derivative changes from positive to negative, then the point where that change occurs is considered to be an inflection point.
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